I keep getting "payment unsuccessful" emails

When a subscription rolls over into a new billing period, an invoice is raised for that period. If the payment can't be collected, the payment processor automatically retries it a few times — and each attempt sends one of these emails. Managing your subscription under Settings → Billing Details stops it from renewing into the next period, but it doesn't remove the invoice already raised for the current one. The retry emails stop on their own once the attempts finish.